Kyle Okposo scored twice, and Zemgus Girgensons had two assists for the Sabres (29-25-8), who are 5-1-0 in their past six games and denied the Jets of a shot on goal in the second half of the third period.
"It's unbelievable really. I'm really thankful for the guys for stepping up like that," said Johansson, a third-round pick (No. 61) by the Sabres in the 2014 NHL Draft. "I don't think we gave up any shot really in the last nine, 10 minutes. That's just unbelievable the way they stepped up there for me and for the rest of the team to get the win."
WATCH: [All Jets vs. Sabres highights]
Blake Wheeler scored and Connor Hellebuyck made 23 saves for the Jets (32-27-5), who have lost two in a row after a three-game winning streak. Winnipeg holds the second wild card into the Stanley Cup Playoffs from the Western Conference, one point ahead of the Calgary Flames, who play Sunday, and the Nashville Predators.
Buffalo trails the Toronto Maple Leafs by six points for third place in the Atlantic Division and the Carolina Hurricanes by eight for the second wild card in the East.
"It doesn't matter who you play now," Jets coach Paul Maurice said. "These guys think they've got a chance to get back into it, so they're playing hard, and their record's better than ours in the last seven or eight, so they're going to be just as hard as beating Washington [on Tuesday]. The opponent isn't nearly as critical as the desperation that we'll need from 18 skaters -- all of them."
Okposo's second goal of the game made it 2-1 with a wrist shot at 7:47 of the third period.